projection of points-engineering graphics

PROJECTION OF POINTS AND LINESPREPARED BY : - B.E.(IT)

EN NO NAME16BEITV120 DHRUNAIVI16BEITV121 PRITEN16BEITV122 ANKUR16BEITV123 DHRUMIL16BEIV124

16BEIV125

DARSHAN

NIKUNJGuided By : -PROF. ROMA PATEL

INFORMATION TECHNOLOGY SVIT,VASAD - 041

PROJECTION OF POINTS

(d) Projections of Right & Regular Solids like; (Prisms, Pyramids, Cylinder and Cone)

SOLID GEOMETRYSOLID GEOMETRYFollowing topics will be covered in Solid Geometry ;(a) Projections of Points in space(b) Projections of Lines (Without H.T. & V.T.)(c) Projections of Planes

(1)In quadrant I (Above H.P & In Front of V.P.)

(2) In quadrant II (Above H.P & Behind V.P.)

(3) In quadrant III (Below H.P & Behind V.P.)

(4) In quadrant IV (Below H.P & In Front of V.P.)

Orientation of Point in SpaceOrientation of Point in Space

(5) In Plane (Above H.P. & In V.P.)

(6) In Plane (Below H.P. & In V.P.)

(7) In Plane ( In H.P. & In front of V.P.)

(8) In Plane ( In H.P. & Behind V.P.)

(9) In Plane ( In H.P. & V.P.)

Orientation of Point in SpaceOrientation of Point in Space

..

..

....

..

XX

YY

aa11’’

AA11

aa11

aa11’’

aa11

YYXX

XX

YY

POSITION: 1 (I Qua.)POSITION: 1 (I Qua.)

POINT POINT

AA11

Above H.P.Above H.P.

In Front Of V.P.In Front Of V.P.

AA11- Point- Pointaa11’- F.V.’- F.V.aa1 1 - T.V.- T.V.

CONCLUSIONS:CONCLUSIONS:

In 3DIn 3D In 2DIn 2D Point, Above Point, Above

H.P.H.P.

Point, In- Front Point, In- Front Of V.P.Of V.P.

T.V.T.V.Below XYBelow XY

F.V.F.V. Above XYAbove XY

(3D)(3D)

(2D)(2D)

..

....

....

POINT POINT

AA22


Behind V.P.Behind V.P.

(3D)(3D)

(2D)(2D)

XX

YY

XX YY

AA22

aa22

aa22’’

aa22

aa22’’

AA22- Point- Point

XX

aa22’- F.V.’- F.V.YY aa2 2 - T.V.- T.V.

CONCLUSIONS:CONCLUSIONS:In 3DIn 3D

Point, Above Point, Above H.P.H.P.

Point, Behind Point, Behind V.P.V.P.

T.V.T.V.Above XYAbove XY


In 2DIn 2D

POSITION:2 (II Qua.)POSITION:2 (II Qua.)

aa33

AA33

POINT POINT

AA33

Below H.P.Below H.P.

Behind V.P.Behind V.P.

aa33’’

XX

YY

..

..aa33

aa33’’

XX

YY

XX YY(2D)(2D)

(3D)(3D)

AA33- Point- Pointaa33’- F.V.’- F.V.aa33- T.V.- T.V.


Point, Below Point, Below H.P.H.P.

Point Behind Point Behind V.P.V.P.


F.V.F.V. Below XYBelow XY

In 2DIn 2D

....

..

POSITION: 3 (III Qua.)POSITION: 3 (III Qua.)

AA44

aa44..aa44’’

..aa44’’

XX

YY

XX

YY

XX YY..

(2D)(2D)

(3D)(3D)

POINT POINT

AA44


In Front of V.P.In Front of V.P.




Point, In Point, In Front Of V.P.Front Of V.P.



In 2DIn 2D

..

..aa44

POSITION: 4 (IV Qua.)POSITION: 4 (IV Qua.)

H.P.H.P.

H.P.H.P. V.P.

V.P...

..

..

..

POINT POINT

AA55


In V.P.In V.P.

In 3DIn 3D In 2DIn 2D Point, Above Point, Above

H.P.H.P.

Point, Point, In V.P.In V.P.

T.V.T.V.On XYOn XY


YY

XX

aa55’’

AA55

aa55

aa55’’

aa55 XX YY

AA55

XX

YY

(3D)(3D)

(2D)(2D)



POSITION: 5 POSITION: 5

..POINT POINT

AA66


In V.P.In V.P.XX

YY

XX

YY

AA66

aa66

aa66’’

aa66’’..

XX YY

(2D)(2D)

aa66

..

AA66

(3D)(3D)

..




Point In V.P.Point In V.P. T.V.T.V.On XYOn XY


In 2DIn 2D

POSITION: 6POSITION: 6

AA77

....

POINT POINT

AA77

In Front of V.P.In Front of V.P.

In H.P.In H.P.

AA77

aa77

aa77’’

XX

YY

YY

XX

(3D)(3D)

(2D)(2D)

YYXX

AA77 Point Point

..

..

aa77’- F.V.’- F.V.

aa77’’

aa77


Point, In- Point, In- Front Of V.P.Front Of V.P.

CONCLUSIONS:CONCLUSIONS:In 3DIn 3D In 2DIn 2D

Point In H.P.Point In H.P. F.V.F.V. On XYOn XY

aa7 7 - T.V.- T.V.


AA88

....

POINT POINT

AA88

In H.P.In H.P.

Behind V.P.Behind V.P.YY

XX

YY

XX

AA88aa88

aa88’’

XX YY

(3D)(3D)

(2D)(2D)

aa88..

..aa88’’


F.V.F.V. On XYOn XY

Point, InPoint, In H.P.H.P.


Point, Behind Point, Behind V.P.V.P.


In 2DIn 2D


POINT POINT

AA99

In VIn V.P..P.

In H.PIn H.P

H.P.H.P.

(3D)(3D)

(2D)(2D)

XX

YY

YYXX

..AA99

AA99- Point- Point

XX

aa99’’

aa99’- F.V.’- F.V.

..aa99’’

aa99

aa99AA99


In 3DIn 3D In 2DIn 2D Point, InPoint, In

H.P.H.P.F.V.F.V.

On XYOn XYT.V.T.V.

On XYOn XYPoint, Point, In V.P.In V.P.

aa9 9 - T.V.- T.V.


PROJECTION OF STRAIT LINE

Definition of Straight lineDefinition of Straight line

A straight line is the shortest distance between two points.

- Top views of two end points of a straight line, when joined, give the top view of the straight line.

- Front views of the two end points of a straight line, when joined, give the front view of the straight line.

- Both the above projections are straight lines.

Orientation of Straight Line in SpaceOrientation of Straight Line in Space

- A line in space may be parallel, perpendicular or inclined to either the H.P. or V.P. or both.

- It may be in one or both the reference Planes.

- Line ends may be in different Quadrants.

- Position of Straight Line in space can be fixed by various combinations of data like distance of its end points from reference planes, inclinations of the line with the reference planes, distance between end projectors of the line etc.

Notations used for Straight Notations used for Straight Line Line

True length of the lineTrue length of the line: Denoted by Capital letters. e.g. AB=100 mm, means that true length of the line is 100 mm.

Front View LengthFront View Length: Denoted by small letters. e.g. a’b’=70 mm, means that Front View Length is 70 mm.

Top View LengthTop View Length: Denoted by small letters. e.g. ab=80 mm, means that Top View Length is 80 mm.Inclination of True Length of Line with H.P.Inclination of True Length of Line with H.P.: It is denoted by θ. e.g. Inclination of the line with H.P. (or Ground) is given as 30º means that θ = 30º.

Inclination of Front View Length with XY Inclination of Front View Length with XY : It is denoted by α. e.g. Inclination of the Front View of the line with XY is given as 50º means that α = 50º.Inclination of Top View Length with XY Inclination of Top View Length with XY :It is denoted by β. e.g. Inclination of the Top View of the line with XY is given as 30º means that β = 30º.End Projector DistanceEnd Projector Distance: It is the distance between two projectors passing through end points of F.V. & T.V. measured parallel to XY line.

Inclination of True Length of Line with V.P.Inclination of True Length of Line with V.P.: It is denoted by Φ. e.g. Inclination of the line with V.P. is given as 40º means that Φ = 40º.

Line in Different Positions with Line in Different Positions with respect to H.P. & V.P.respect to H.P. & V.P.

CLASS A: Line perpendicular to (or in) one CLASS A: Line perpendicular to (or in) one reference plane & hence parallel to reference plane & hence parallel to both the other planes both the other planes

(1)(1) Line perpendicular to P.P. & (hence) parallel Line perpendicular to P.P. & (hence) parallel to both H.P. & V.P.to both H.P. & V.P.

(2) Line perpendicular to V.P. & (hence) parallel(2) Line perpendicular to V.P. & (hence) parallel to both H.P. & P.P.to both H.P. & P.P.

(3) Line perpendicular to H.P. & (hence) parallel(3) Line perpendicular to H.P. & (hence) parallel to both V.P. & P.P.to both V.P. & P.P.


CLASS B: Line parallel to (or in) one CLASS B: Line parallel to (or in) one reference plane & inclined to other reference plane & inclined to other two two planesplanes

(1)(1) Line parallel to ( or in) V.P. & inclined to H.P.Line parallel to ( or in) V.P. & inclined to H.P. by by ..

(2) Line parallel to ( or in) H.P. & inclined to V.P.(2) Line parallel to ( or in) H.P. & inclined to V.P. by by ..

(3) Line parallel to ( or in) P.P. & inclined to H.P.(3) Line parallel to ( or in) P.P. & inclined to H.P. by by & V.P. by & V.P. by ..


CLASS C: Line inclined to all three reference CLASS C: Line inclined to all three reference planes ( Oblique lines )planes ( Oblique lines )

Line inclined to H.P. by Line inclined to H.P. by , to V.P. by , to V.P. by and also inclined and also inclined to profile plane.to profile plane.

P.P..

H.P.

V.P.

Y

X

BA

a’

b’

ba

b”a”

z x

Y

Class A(1) : Line perpendicular to P.P. & hence Class A(1) : Line perpendicular to P.P. & hence parallel to both the other planes parallel to both the other planes

XX

YY

a’a’

b’b’H.P.H.P.

V.P.V.P.

aabb

Line perpendicular to P.P. & hence parallel to both Line perpendicular to P.P. & hence parallel to both the other planesthe other planes

P.P.P.P.

a”, b”a”, b”

YY11

..

H.P.H.P.

V.P.V.P.

a’a’b’b’

aabb

XX

YY

Line perpendicular to P.P. & hence parallel to both Line perpendicular to P.P. & hence parallel to both the other planesthe other planes

V.P.V.P.

H.P.H.P.

YY

XX

AA

BB

bb

aa

a’, b’a’, b’..

XX

Class A(2):Line perpendicular to V.P. & (hence) Class A(2):Line perpendicular to V.P. & (hence) parallel to both the other Planesparallel to both the other Planes(i.e. H.P. & P.P.)(i.e. H.P. & P.P.)

a’, b’a’, b’

XX

YY

V.P.V.P.

H.P.H.P.

aa

bb

..

Line perpendicular to V.P. & (hence) parallel to both Line perpendicular to V.P. & (hence) parallel to both the other Planesthe other Planes

H.P.H.P.

V.P.V.P.

P.P.P.P.

Class B(3): Line parallel to (or contained by) P.P., inclined to Class B(3): Line parallel to (or contained by) P.P., inclined to H.P. by H.P. by & to V.P. by & to V.P. by

YY

XX

AA

BB

a”a”

b”b”

YY

XXZZbb

aa

bb’’

aa’’

H.P.H.P.

V.PV.P..

XX

YY

aa bb

a’a’

b’b’

YY

XX

BB

AA

Class C : Line inclined to H.P. by Class C : Line inclined to H.P. by & V.P. by & V.P. by ( ( i.e. Line inclined to both the planes)i.e. Line inclined to both the planes)

V.P.V.P.

H.PH.P..

P.P.P.P.

Class B(3): Line parallel to (or contained by) P.P., Class B(3): Line parallel to (or contained by) P.P., inclined to H.P. by inclined to H.P. by & to V.P. by & to V.P. by

XX YY

a’a’

b’b’

aa

bb

bb””

a”a”

projection of points-engineering graphics

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